Finite Energy Global Solutions to a Two-fluid Model Arising in Superfluidity
Vol. 10 No. 3 (2015) P.349~P.373
In this paper we study a hydrodynamic system describing two interacting fluids,
which can be seen as a toy model to start an investigation on the so called two-fluid models
arising in superfluidity and Bose-Einstein condensates at finite temperatures. We show
global existence of finite energy weak solutions, by using a fractional step argument which combines the study of a Cauchy problem for an appropriate nonlinear Schrödinger equation and the polar factorisation techinque. The convergence of the sequence of approximate solutions is then proved by using the dispersive properties of the nonlinear Schrödinger equation.
Quantum Hydrodynamics, Two- uid models, Superfluidity.
MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 35Q40, 35Q55, 76Y05.
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Revised : 2015-05-29